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Differenciált termékes Bertrand-oligopóliumban…

a reakciófüggvények nem metszik egymást.

azonos határköltség esetén a vállalatok egyensúlyban nem ugyanannyit termelnek.

a vállalatok szimultán döntenek.

egy vállalat profitfüggvényének szakadása van.

minden vásárló az olcsóbban áruló vállalattól vásárol.

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Which of the following would be a valid partition of the set of all strings A^* over the alphabet $A = \{a, b\}$ A = \{a, b\}?

$\{ A^n : n\in\mathbb{N} \}$ \{ A^n : n\in\mathbb{N} \}

$\{\{\epsilon\},\{\text{all strings starting with a}\}, \{\text{all strings starting with b}\}\}$ \{\{\epsilon\},\{\text{all strings starting with a}\}, \{\text{all strings starting with b}\}\}

$\{\{\text{aa}\},\{\text{ab}\}, \{\text{ba}\}, \{\text{bb}\}\}$ \{\{\text{aa}\},\{\text{ab}\}, \{\text{ba}\}, \{\text{bb}\}\}

There is no way of partitioning the set, because it's an infinite set.

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Which of the following Boolean expressions is equivalent to $\neg (\neg A \vee \neg B) \vee C$ \neg (\neg A \vee \neg B) \vee C?

$(A \wedge C) \vee (B \wedge C)$ (A \wedge C) \vee (B \wedge C)

$(\neg A \vee C) \wedge (\neg B \vee C)$ (\neg A \vee C) \wedge (\neg B \vee C)

$(A \vee C) \wedge (B \vee C)$ (A \vee C) \wedge (B \vee C)

$(\neg A \wedge C) \vee (\neg B \wedge C)$ (\neg A \wedge C) \vee (\neg B \wedge C)

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Suppose you have:

a function f(A) which takes some finite set of strings A as input, and outputs the cardinality of A; and
a function g(B, C) which takes two finite sets of strings B and C as input, and outputs the Cartesian product $B \times C$ B \times C.

Which of the following statements is true?

$g \circ f$ g \circ f is defined, but $f \circ g$ f \circ g is not.

Both $g \circ f$ g \circ f and $f \circ g$ f \circ g are defined.

Neither $g \circ f$ g \circ f nor $f \circ g$ f \circ g are defined.

$f \circ g$ f \circ g is defined, but $g \circ f$ g \circ f is not.

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Let:

B be the set of all possible bijections;

S be the set of all possible surjections;

I be the set of all possible injections; and

J be the set of all possible identity functions.

Which of the following statements is true?

$J \cap (I \triangle S) = \emptyset$ J \cap (I \triangle S) = \emptyset

$B \cap (I \cap S) = \emptyset$ B \cap (I \cap S) = \emptyset

$B \cap (I \cup S) = \emptyset$ B \cap (I \cup S) = \emptyset

$J \cap B = \emptyset$ J \cap B = \emptyset

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Let A be the alphabet $\{a, b\}$ \{a, b\}.

Consider the following function definition.

$f: A^* \rightarrow \mathbb{N}_0$ f: A^* \rightarrow \mathbb{N}_0

f(x) = |x|

Which of the following is true about f?

It is neither injective, surjective, nor bijective.

It is injective, but not surjective.

It is bijective.

It is surjective, but not injective.

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